2017/08/22 by Andrea Coladangelo, Coladangelo, Andrea, Jalex Stark +1 · 2 citations
Computer Science · Physics and Astronomy · #Computability, Logic, AI Algorithms #FOS: Physical sciences #Machine Learning and Algorithms #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.1708.06522
18 pages
arxiv created 2017/08/22 · openalex publication_date 2017/08/22 · arxiv updated 2017/08/23 · openalex created_date 2022/09/14 · openalex updated_date 2026/07/28
Completely determining the relationship between quantum correlation sets is a long-standing open problem, known as Tsirelson's problem. Following recent progress by Slofstra [arXiv:1606.03140 (2016), arXiv:1703.08618 (2017)] only two instances of the problem remain open. One of them is the question of whether the set of finite-dimensional quantum correlations is strictly contained in the set of infinite-dimensional ones (i.e. whether \mathcal Cq ≠ \mathcal Cqs). The usual formulation of the question assumes finite question and answer sets. In this work, we show that, when one allows for either infinite answer sets (and finite question sets) or infinite question sets (and finite answer sets), there exist correlations that are achievable using an infinite-dimensional quantum strategy, but not a finite-dimensional one. For the former case, our proof exploits a recent result [Nat. Comm. 8, 15485 (2017)], which shows self-testing of any pure bipartite entangled state of arbitrary local dimension d, using question sets of size 3 and 4 and answer sets of size d. For the latter case, a key step in our proof is to show a novel self-test, inspired by [Nat. Comm. 8, 15485 (2017)], of all bipartite entangled states of any local dimension d, using question sets of size O(d), and answer sets of size 4 and 3 respectively.